Download 5.7 Slope-Intercept Form

 Learn
to use slopes and
intercepts to graph linear
equations.

X-intercept - the x- coordinate of the point

where the line intersects the x-axis. The ycoordinate of this point is always 0 (3,0).
Y-intercept – the y-coordinate of the point
where the line intersects the y-axis. The xcoordinate of this point is always 0 (0,5).

Slope-intercept form – when a linear equation
is written as y = mx + b. m is the slope and b is
the y-intercept of the line.
Finding Intercepts
Find the x-intercept and y-intercept.
y
A.
The line intersects the
x-axis at (2,0).
4
2
x
–4 –2
–2
–4
0
2
4
The x-intercept is 2.
The line intersects
the x-axis at (–4).
The y-intercept is –4.
Finding Intercepts
Find the x-intercept and y-intercept.
y
B.
The line intersects the
x-axis at (4,0).
4
2
x
–4 –2
–2
–4
0
2
4
The x-intercept is 4.
The line intersects the
x-axis at (0, 1).
The y-intercept is 1.
Slope-Intercept Form
The linear equation y = mx + b is written
in slope-intercept form, where m is the
slope and b is the y-intercept of the line.
y = mx + b
Slope
y-intercept
Graphing w/Slope-Intercept
Form
Graph the equation.
1
y= x+1
3
Step 1: Find m and b.
y= 1x+1
3
Step 2: Plot (0, 1)‫‏‬
m=1
3
b= 1
1
Step 3: Use the slope to plot at least 1
3
more point on the line.
Graphing w/Slope-Intercept
Form
Graph the equation.
1
y= x+1
3
y
4
2
x
–4 –2
–2
0
2
4
–4
Step 4: Draw a line through the points.
Not Slope-Intercept Form?
Graph the equation.
B. 3x + y = 5
Step 1: Find m and b.
3x + y = 5
– 3x
= – 3x
y = 5 – 3x
y = –3x + 5
m = –3
b=5
Now Graph It!
Step 2: Plot (0, 5)‫‏‬
Step 3: Use the slope –3
to plot at least 1 more
point on the line.
Step 4: Draw a line
through the points.
What To Do, What To Do…
Graph the equation.
2x + y = 4
Step 1: Find m and b.
2x + y = 4
– 2x
= – 2x
y = 4 – 2x
y = –2x + 4
m = –2
b=4
And the Graph…
Step 2: Plot (0, 4)‫‏‬
Step 3: Use the slope –2
to plot at least 1 more
point on the line.
Step 4: Draw a line
through the points.
Write the Equation
Write the equation of the line in slope-intercept
form.
The line rises from right to
left so the slope is negative.
m = rise = - 2
5
run
The line intersects the y-axis
at (0, -4), so the y-intercept
is -4.
b = –4
Substitute for m and b.
x–4
y= 2
5
And Another One…
Write the equation of the line in slope-intercept
form.
The line rises from left to
right so the slope is positive.
m = rise =
run
1
2
The line intersects the y-axis
at (0, 2), so the y-intercept
is 2.
b=2
Substitute for m and b.
x+2
y= 1
2
Spiders and Slope-Intercept
Form
A spider descends a 20-foot drainpipe at a rate
of 2 feet per minute. The linear equation y = –
2x + 20 represents the distance y the spider
has left to descend after x minutes. Graph the
equation, and then identify the x- and yintercepts and describe their meaning.
Use the slope and y-intercept to
graph the equation.
Plot (0, 20). Use the slope -2 to plot
the line down to the x-axis.
The y-intercept is 20. This represents
the total distance in feet the spider
has to descend.
The x-intercept is 10. This represents
the time in minutes it takes the
spider has to descend the 20 ft.
Distance remaining (ft)‫‏‬
Spiders and Slope-Intercept
Form
Spider's Decent
20
18
16
14
12
10
8
6
4
2
2 4 6 8 10 12 14 16
Time (min)‫‏‬
Exit Ticket
3
1. Graph y = x – 3. Identify the x- and y8
intercepts.
y
8
4
x
–8 –4
–4
0
4
8
–8
x-int. = 8, y-int. = –3